LMFDB - Embedded newform 1850.2.b.l.149.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(149,1850)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1850.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 370)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.4
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1850.149
Dual form			1850.2.b.l.149.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +0.732051i q^{3} -1.00000 q^{4} -0.732051 q^{6} +4.73205i q^{7} -1.00000i q^{8} +2.46410 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +0.732051i q^{3} -1.00000 q^{4} -0.732051 q^{6} +4.73205i q^{7} -1.00000i q^{8} +2.46410 q^{9} -5.46410 q^{11} -0.732051i q^{12} -5.46410i q^{13} -4.73205 q^{14} +1.00000 q^{16} -5.46410i q^{17} +2.46410i q^{18} -6.19615 q^{19} -3.46410 q^{21} -5.46410i q^{22} -8.00000i q^{23} +0.732051 q^{24} +5.46410 q^{26} +4.00000i q^{27} -4.73205i q^{28} -4.92820 q^{29} +0.732051 q^{31} +1.00000i q^{32} -4.00000i q^{33} +5.46410 q^{34} -2.46410 q^{36} -1.00000i q^{37} -6.19615i q^{38} +4.00000 q^{39} -2.00000 q^{41} -3.46410i q^{42} +6.92820i q^{43} +5.46410 q^{44} +8.00000 q^{46} +4.73205i q^{47} +0.732051i q^{48} -15.3923 q^{49} +4.00000 q^{51} +5.46410i q^{52} -6.00000i q^{53} -4.00000 q^{54} +4.73205 q^{56} -4.53590i q^{57} -4.92820i q^{58} +10.1962 q^{59} -4.92820 q^{61} +0.732051i q^{62} +11.6603i q^{63} -1.00000 q^{64} +4.00000 q^{66} +3.66025i q^{67} +5.46410i q^{68} +5.85641 q^{69} +2.92820 q^{71} -2.46410i q^{72} -0.928203i q^{73} +1.00000 q^{74} +6.19615 q^{76} -25.8564i q^{77} +4.00000i q^{78} -8.73205 q^{79} +4.46410 q^{81} -2.00000i q^{82} -8.73205i q^{83} +3.46410 q^{84} -6.92820 q^{86} -3.60770i q^{87} +5.46410i q^{88} +2.00000 q^{89} +25.8564 q^{91} +8.00000i q^{92} +0.535898i q^{93} -4.73205 q^{94} -0.732051 q^{96} +2.00000i q^{97} -15.3923i q^{98} -13.4641 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} - 8 q^{11} - 12 q^{14} + 4 q^{16} - 4 q^{19} - 4 q^{24} + 8 q^{26} + 8 q^{29} - 4 q^{31} + 8 q^{34} + 4 q^{36} + 16 q^{39} - 8 q^{41} + 8 q^{44} + 32 q^{46} - 20 q^{49} + 16 q^{51} - 16 q^{54} + 12 q^{56} + 20 q^{59} + 8 q^{61} - 4 q^{64} + 16 q^{66} - 32 q^{69} - 16 q^{71} + 4 q^{74} + 4 q^{76} - 28 q^{79} + 4 q^{81} + 8 q^{89} + 48 q^{91} - 12 q^{94} + 4 q^{96} - 40 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 - 8 * q^11 - 12 * q^14 + 4 * q^16 - 4 * q^19 - 4 * q^24 + 8 * q^26 + 8 * q^29 - 4 * q^31 + 8 * q^34 + 4 * q^36 + 16 * q^39 - 8 * q^41 + 8 * q^44 + 32 * q^46 - 20 * q^49 + 16 * q^51 - 16 * q^54 + 12 * q^56 + 20 * q^59 + 8 * q^61 - 4 * q^64 + 16 * q^66 - 32 * q^69 - 16 * q^71 + 4 * q^74 + 4 * q^76 - 28 * q^79 + 4 * q^81 + 8 * q^89 + 48 * q^91 - 12 * q^94 + 4 * q^96 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times$.

$n$	$1001$	$1777$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	0.732051i	0.422650i	0.977416	+	0.211325i	$0.0677778\pi$
$3$	0.732051i	0.422650i	−0.977416	+	0.211325i	$0.932222\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−0.732051	−0.298858
$7$	4.73205i	1.78855i	0.447521	+	0.894274i	$0.352307\pi$
$7$	4.73205i	1.78855i	−0.447521	+	0.894274i	$0.647693\pi$
$8$	− 1.00000i	− 0.353553i
$9$	2.46410	0.821367
$10$	0	0
$11$	−5.46410	−1.64749	−0.823744	−	0.566961i	$-0.808119\pi$
$11$	−5.46410	−1.64749	−0.823744	+	0.566961i	$0.808119\pi$
$12$	− 0.732051i	− 0.211325i
$13$	− 5.46410i	− 1.51547i	−0.652563	−	0.757735i	$-0.726306\pi$
$13$	− 5.46410i	− 1.51547i	0.652563	−	0.757735i	$-0.273694\pi$
$14$	−4.73205	−1.26469
$15$	0	0
$16$	1.00000	0.250000
$17$	− 5.46410i	− 1.32524i	−0.748956	−	0.662620i	$-0.769445\pi$
$17$	− 5.46410i	− 1.32524i	0.748956	−	0.662620i	$-0.230555\pi$
$18$	2.46410i	0.580794i
$19$	−6.19615	−1.42149	−0.710747	−	0.703447i	$-0.751643\pi$
$19$	−6.19615	−1.42149	−0.710747	+	0.703447i	$0.751643\pi$
$20$	0	0
$21$	−3.46410	−0.755929
$22$	− 5.46410i	− 1.16495i
$23$	− 8.00000i	− 1.66812i	−0.551677	−	0.834058i	$-0.686012\pi$
$23$	− 8.00000i	− 1.66812i	0.551677	−	0.834058i	$-0.313988\pi$
$24$	0.732051	0.149429
$25$	0	0
$26$	5.46410	1.07160
$27$	4.00000i	0.769800i
$28$	− 4.73205i	− 0.894274i
$29$	−4.92820	−0.915144	−0.457572	−	0.889172i	$-0.651281\pi$
$29$	−4.92820	−0.915144	−0.457572	+	0.889172i	$0.651281\pi$
$30$	0	0
$31$	0.732051	0.131480	0.0657401	−	0.997837i	$-0.479059\pi$
$31$	0.732051	0.131480	0.0657401	+	0.997837i	$0.479059\pi$
$32$	1.00000i	0.176777i
$33$	− 4.00000i	− 0.696311i
$34$	5.46410	0.937086
$35$	0	0
$36$	−2.46410	−0.410684
$37$	− 1.00000i	− 0.164399i
$37$	− 1.00000i	− 0.164399i
$38$	− 6.19615i	− 1.00515i
$39$	4.00000	0.640513
$40$	0	0
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	− 3.46410i	− 0.534522i
$43$	6.92820i	1.05654i	0.849076	+	0.528271i	$0.177159\pi$
$43$	6.92820i	1.05654i	−0.849076	+	0.528271i	$0.822841\pi$
$44$	5.46410	0.823744
$45$	0	0
$46$	8.00000	1.17954
$47$	4.73205i	0.690241i	0.938558	+	0.345120i	$0.112162\pi$
$47$	4.73205i	0.690241i	−0.938558	+	0.345120i	$0.887838\pi$
$48$	0.732051i	0.105662i
$49$	−15.3923	−2.19890
$50$	0	0
$51$	4.00000	0.560112
$52$	5.46410i	0.757735i
$53$	− 6.00000i	− 0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$	− 6.00000i	− 0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	−4.00000	−0.544331
$55$	0	0
$56$	4.73205	0.632347
$57$	− 4.53590i	− 0.600794i
$58$	− 4.92820i	− 0.647105i
$59$	10.1962	1.32743	0.663713	−	0.747987i	$-0.268980\pi$
$59$	10.1962	1.32743	0.663713	+	0.747987i	$0.268980\pi$
$60$	0	0
$61$	−4.92820	−0.630992	−0.315496	−	0.948927i	$-0.602171\pi$
$61$	−4.92820	−0.630992	−0.315496	+	0.948927i	$0.602171\pi$
$62$	0.732051i	0.0929705i
$63$	11.6603i	1.46905i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	4.00000	0.492366
$67$	3.66025i	0.447171i	0.974684	+	0.223586i	$0.0717762\pi$
$67$	3.66025i	0.447171i	−0.974684	+	0.223586i	$0.928224\pi$
$68$	5.46410i	0.662620i
$69$	5.85641	0.705028
$70$	0	0
$71$	2.92820	0.347514	0.173757	−	0.984789i	$-0.444409\pi$
$71$	2.92820	0.347514	0.173757	+	0.984789i	$0.444409\pi$
$72$	− 2.46410i	− 0.290397i
$73$	− 0.928203i	− 0.108638i	−0.998524	−	0.0543190i	$-0.982701\pi$
$73$	− 0.928203i	− 0.108638i	0.998524	−	0.0543190i	$-0.0172988\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	6.19615	0.710747
$77$	− 25.8564i	− 2.94661i
$78$	4.00000i	0.452911i
$79$	−8.73205	−0.982432	−0.491216	−	0.871038i	$-0.663448\pi$
$79$	−8.73205	−0.982432	−0.491216	+	0.871038i	$0.663448\pi$
$80$	0	0
$81$	4.46410	0.496011
$82$	− 2.00000i	− 0.220863i
$83$	− 8.73205i	− 0.958467i	−0.877687	−	0.479234i	$-0.840915\pi$
$83$	− 8.73205i	− 0.958467i	0.877687	−	0.479234i	$-0.159085\pi$
$84$	3.46410	0.377964
$85$	0	0
$86$	−6.92820	−0.747087
$87$	− 3.60770i	− 0.386786i
$88$	5.46410i	0.582475i
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	25.8564	2.71049
$92$	8.00000i	0.834058i
$93$	0.535898i	0.0555701i
$94$	−4.73205	−0.488074
$95$	0	0
$96$	−0.732051	−0.0747146
$97$	2.00000i	0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$	2.00000i	0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$	− 15.3923i	− 1.55486i
$99$	−13.4641	−1.35319
$100$	0	0
$101$	−9.46410	−0.941713	−0.470857	−	0.882210i	$-0.656055\pi$
$101$	−9.46410	−0.941713	−0.470857	+	0.882210i	$0.656055\pi$
$102$	4.00000i	0.396059i
$103$	− 6.53590i	− 0.644001i	−0.946739	−	0.322001i	$-0.895645\pi$
$103$	− 6.53590i	− 0.644001i	0.946739	−	0.322001i	$-0.104355\pi$
$104$	−5.46410	−0.535799
$105$	0	0
$106$	6.00000	0.582772
$107$	− 3.26795i	− 0.315925i	−0.987445	−	0.157962i	$-0.949508\pi$
$107$	− 3.26795i	− 0.315925i	0.987445	−	0.157962i	$-0.0504924\pi$
$108$	− 4.00000i	− 0.384900i
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	0	0
$111$	0.732051	0.0694832
$112$	4.73205i	0.447137i
$113$	− 10.5359i	− 0.991134i	−0.868570	−	0.495567i	$-0.834960\pi$
$113$	− 10.5359i	− 0.991134i	0.868570	−	0.495567i	$-0.165040\pi$
$114$	4.53590	0.424826
$115$	0	0
$116$	4.92820	0.457572
$117$	− 13.4641i	− 1.24476i
$118$	10.1962i	0.938632i
$119$	25.8564	2.37025
$120$	0	0
$121$	18.8564	1.71422
$122$	− 4.92820i	− 0.446179i
$123$	− 1.46410i	− 0.132014i
$124$	−0.732051	−0.0657401
$125$	0	0
$126$	−11.6603	−1.03878
$127$	− 3.66025i	− 0.324795i	−0.986725	−	0.162398i	$-0.948077\pi$
$127$	− 3.66025i	− 0.324795i	0.986725	−	0.162398i	$-0.0519227\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−5.07180	−0.446547
$130$	0	0
$131$	−18.5885	−1.62408	−0.812041	−	0.583601i	$-0.801643\pi$
$131$	−18.5885	−1.62408	−0.812041	+	0.583601i	$0.801643\pi$
$132$	4.00000i	0.348155i
$133$	− 29.3205i	− 2.54241i
$134$	−3.66025	−0.316198
$135$	0	0
$136$	−5.46410	−0.468543
$137$	− 2.00000i	− 0.170872i	−0.996344	−	0.0854358i	$-0.972772\pi$
$137$	− 2.00000i	− 0.170872i	0.996344	−	0.0854358i	$-0.0272282\pi$
$138$	5.85641i	0.498530i
$139$	−6.92820	−0.587643	−0.293821	−	0.955860i	$-0.594927\pi$
$139$	−6.92820	−0.587643	−0.293821	+	0.955860i	$0.594927\pi$
$140$	0	0
$141$	−3.46410	−0.291730
$142$	2.92820i	0.245729i
$143$	29.8564i	2.49672i
$144$	2.46410	0.205342
$145$	0	0
$146$	0.928203	0.0768186
$147$	− 11.2679i	− 0.929365i
$148$	1.00000i	0.0821995i
$149$	−4.39230	−0.359832	−0.179916	−	0.983682i	$-0.557583\pi$
$149$	−4.39230	−0.359832	−0.179916	+	0.983682i	$0.557583\pi$
$150$	0	0
$151$	−12.3923	−1.00847	−0.504236	−	0.863566i	$-0.668226\pi$
$151$	−12.3923	−1.00847	−0.504236	+	0.863566i	$0.668226\pi$
$152$	6.19615i	0.502574i
$153$	− 13.4641i	− 1.08851i
$154$	25.8564	2.08357
$155$	0	0
$156$	−4.00000	−0.320256
$157$	− 3.07180i	− 0.245156i	−0.992459	−	0.122578i	$-0.960884\pi$
$157$	− 3.07180i	− 0.245156i	0.992459	−	0.122578i	$-0.0391162\pi$
$158$	− 8.73205i	− 0.694685i
$159$	4.39230	0.348332
$160$	0	0
$161$	37.8564	2.98350
$162$	4.46410i	0.350733i
$163$	− 11.3205i	− 0.886691i	−0.896351	−	0.443345i	$-0.853792\pi$
$163$	− 11.3205i	− 0.886691i	0.896351	−	0.443345i	$-0.146208\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	8.73205	0.677739
$167$	1.46410i	0.113296i	0.998394	+	0.0566478i	$0.0180412\pi$
$167$	1.46410i	0.113296i	−0.998394	+	0.0566478i	$0.981959\pi$
$168$	3.46410i	0.267261i
$169$	−16.8564	−1.29665
$170$	0	0
$171$	−15.2679	−1.16757
$172$	− 6.92820i	− 0.528271i
$173$	10.0000i	0.760286i	0.924928	+	0.380143i	$0.124125\pi$
$173$	10.0000i	0.760286i	−0.924928	+	0.380143i	$0.875875\pi$
$174$	3.60770	0.273499
$175$	0	0
$176$	−5.46410	−0.411872
$177$	7.46410i	0.561036i
$178$	2.00000i	0.149906i
$179$	0.339746	0.0253938	0.0126969	−	0.999919i	$-0.495958\pi$
$179$	0.339746	0.0253938	0.0126969	+	0.999919i	$0.495958\pi$
$180$	0	0
$181$	5.46410	0.406143	0.203072	−	0.979164i	$-0.434908\pi$
$181$	5.46410	0.406143	0.203072	+	0.979164i	$0.434908\pi$
$182$	25.8564i	1.91660i
$183$	− 3.60770i	− 0.266688i
$184$	−8.00000	−0.589768
$185$	0	0
$186$	−0.535898	−0.0392940
$187$	29.8564i	2.18332i
$188$	− 4.73205i	− 0.345120i
$189$	−18.9282	−1.37682
$190$	0	0
$191$	−8.73205	−0.631829	−0.315915	−	0.948788i	$-0.602311\pi$
$191$	−8.73205	−0.631829	−0.315915	+	0.948788i	$0.602311\pi$
$192$	− 0.732051i	− 0.0528312i
$193$	15.8564i	1.14137i	0.821169	+	0.570685i	$0.193322\pi$
$193$	15.8564i	1.14137i	−0.821169	+	0.570685i	$0.806678\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	15.3923	1.09945
$197$	22.7846i	1.62334i	0.584119	+	0.811668i	$0.301440\pi$
$197$	22.7846i	1.62334i	−0.584119	+	0.811668i	$0.698560\pi$
$198$	− 13.4641i	− 0.956852i
$199$	12.0526	0.854383	0.427192	−	0.904161i	$-0.359503\pi$
$199$	12.0526	0.854383	0.427192	+	0.904161i	$0.359503\pi$
$200$	0	0
$201$	−2.67949	−0.188997
$202$	− 9.46410i	− 0.665892i
$203$	− 23.3205i	− 1.63678i
$204$	−4.00000	−0.280056
$205$	0	0
$206$	6.53590	0.455378
$207$	− 19.7128i	− 1.37014i
$208$	− 5.46410i	− 0.378867i
$209$	33.8564	2.34190
$210$	0	0
$211$	−17.8564	−1.22929	−0.614643	−	0.788806i	$-0.710700\pi$
$211$	−17.8564	−1.22929	−0.614643	+	0.788806i	$0.710700\pi$
$212$	6.00000i	0.412082i
$213$	2.14359i	0.146877i
$214$	3.26795	0.223392
$215$	0	0
$216$	4.00000	0.272166
$217$	3.46410i	0.235159i
$218$	− 2.00000i	− 0.135457i
$219$	0.679492	0.0459158
$220$	0	0
$221$	−29.8564	−2.00836
$222$	0.732051i	0.0491320i
$223$	16.0526i	1.07496i	0.843277	+	0.537479i	$0.180623\pi$
$223$	16.0526i	1.07496i	−0.843277	+	0.537479i	$0.819377\pi$
$224$	−4.73205	−0.316173
$225$	0	0
$226$	10.5359	0.700838
$227$	− 24.3923i	− 1.61897i	−0.587138	−	0.809487i	$-0.699745\pi$
$227$	− 24.3923i	− 1.61897i	0.587138	−	0.809487i	$-0.300255\pi$
$228$	4.53590i	0.300397i
$229$	11.8564	0.783493	0.391747	−	0.920073i	$-0.371871\pi$
$229$	11.8564	0.783493	0.391747	+	0.920073i	$0.371871\pi$
$230$	0	0
$231$	18.9282	1.24538
$232$	4.92820i	0.323552i
$233$	28.9282i	1.89515i	0.319534	+	0.947575i	$0.396474\pi$
$233$	28.9282i	1.89515i	−0.319534	+	0.947575i	$0.603526\pi$
$234$	13.4641	0.880176
$235$	0	0
$236$	−10.1962	−0.663713
$237$	− 6.39230i	− 0.415225i
$238$	25.8564i	1.67602i
$239$	20.7321	1.34104	0.670522	−	0.741889i	$-0.266070\pi$
$239$	20.7321	1.34104	0.670522	+	0.741889i	$0.266070\pi$
$240$	0	0
$241$	4.92820	0.317453	0.158727	−	0.987323i	$-0.449261\pi$
$241$	4.92820	0.317453	0.158727	+	0.987323i	$0.449261\pi$
$242$	18.8564i	1.21214i
$243$	15.2679i	0.979439i
$244$	4.92820	0.315496
$245$	0	0
$246$	1.46410	0.0933477
$247$	33.8564i	2.15423i
$248$	− 0.732051i	− 0.0464853i
$249$	6.39230	0.405096
$250$	0	0
$251$	19.2679	1.21618	0.608091	−	0.793867i	$-0.291936\pi$
$251$	19.2679	1.21618	0.608091	+	0.793867i	$0.291936\pi$
$252$	− 11.6603i	− 0.734527i
$253$	43.7128i	2.74820i
$254$	3.66025	0.229665
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.5359i	1.15624i	0.815953	+	0.578119i	$0.196213\pi$
$257$	18.5359i	1.15624i	−0.815953	+	0.578119i	$0.803787\pi$
$258$	− 5.07180i	− 0.315756i
$259$	4.73205	0.294035
$260$	0	0
$261$	−12.1436	−0.751670
$262$	− 18.5885i	− 1.14840i
$263$	− 8.05256i	− 0.496542i	−0.968691	−	0.248271i	$-0.920138\pi$
$263$	− 8.05256i	− 0.496542i	0.968691	−	0.248271i	$-0.0798624\pi$
$264$	−4.00000	−0.246183
$265$	0	0
$266$	29.3205	1.79776
$267$	1.46410i	0.0896016i
$268$	− 3.66025i	− 0.223586i
$269$	−20.3923	−1.24334	−0.621670	−	0.783279i	$-0.713546\pi$
$269$	−20.3923	−1.24334	−0.621670	+	0.783279i	$0.713546\pi$
$270$	0	0
$271$	−24.7846	−1.50556	−0.752779	−	0.658273i	$-0.771287\pi$
$271$	−24.7846	−1.50556	−0.752779	+	0.658273i	$0.771287\pi$
$272$	− 5.46410i	− 0.331310i
$273$	18.9282i	1.14559i
$274$	2.00000	0.120824
$275$	0	0
$276$	−5.85641	−0.352514
$277$	− 22.2487i	− 1.33680i	−0.743804	−	0.668398i	$-0.766980\pi$
$277$	− 22.2487i	− 1.33680i	0.743804	−	0.668398i	$-0.233020\pi$
$278$	− 6.92820i	− 0.415526i
$279$	1.80385	0.107994
$280$	0	0
$281$	−8.92820	−0.532612	−0.266306	−	0.963889i	$-0.585803\pi$
$281$	−8.92820	−0.532612	−0.266306	+	0.963889i	$0.585803\pi$
$282$	− 3.46410i	− 0.206284i
$283$	16.3923i	0.974421i	0.873284	+	0.487211i	$0.161986\pi$
$283$	16.3923i	0.974421i	−0.873284	+	0.487211i	$0.838014\pi$
$284$	−2.92820	−0.173757
$285$	0	0
$286$	−29.8564	−1.76545
$287$	− 9.46410i	− 0.558648i
$288$	2.46410i	0.145199i
$289$	−12.8564	−0.756259
$290$	0	0
$291$	−1.46410	−0.0858272
$292$	0.928203i	0.0543190i
$293$	6.00000i	0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$	6.00000i	0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$	11.2679	0.657160
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	− 21.8564i	− 1.26824i
$298$	− 4.39230i	− 0.254439i
$299$	−43.7128	−2.52798
$300$	0	0
$301$	−32.7846	−1.88967
$302$	− 12.3923i	− 0.713097i
$303$	− 6.92820i	− 0.398015i
$304$	−6.19615	−0.355374
$305$	0	0
$306$	13.4641	0.769691
$307$	− 18.5885i	− 1.06090i	−0.847716	−	0.530450i	$-0.822023\pi$
$307$	− 18.5885i	− 1.06090i	0.847716	−	0.530450i	$-0.177977\pi$
$308$	25.8564i	1.47331i
$309$	4.78461	0.272187
$310$	0	0
$311$	2.87564	0.163063	0.0815314	−	0.996671i	$-0.474019\pi$
$311$	2.87564	0.163063	0.0815314	+	0.996671i	$0.474019\pi$
$312$	− 4.00000i	− 0.226455i
$313$	− 23.8564i	− 1.34844i	−0.738529	−	0.674222i	$-0.764479\pi$
$313$	− 23.8564i	− 1.34844i	0.738529	−	0.674222i	$-0.235521\pi$
$314$	3.07180	0.173352
$315$	0	0
$316$	8.73205	0.491216
$317$	4.14359i	0.232727i	0.993207	+	0.116364i	$0.0371238\pi$
$317$	4.14359i	0.232727i	−0.993207	+	0.116364i	$0.962876\pi$
$318$	4.39230i	0.246308i
$319$	26.9282	1.50769
$320$	0	0
$321$	2.39230	0.133525
$322$	37.8564i	2.10966i
$323$	33.8564i	1.88382i
$324$	−4.46410	−0.248006
$325$	0	0
$326$	11.3205	0.626985
$327$	− 1.46410i	− 0.0809650i
$328$	2.00000i	0.110432i
$329$	−22.3923	−1.23453
$330$	0	0
$331$	−33.1244	−1.82068	−0.910340	−	0.413862i	$-0.864180\pi$
$331$	−33.1244	−1.82068	−0.910340	+	0.413862i	$0.864180\pi$
$332$	8.73205i	0.479234i
$333$	− 2.46410i	− 0.135032i
$334$	−1.46410	−0.0801121
$335$	0	0
$336$	−3.46410	−0.188982
$337$	− 26.0000i	− 1.41631i	−0.706057	−	0.708155i	$-0.749528\pi$
$337$	− 26.0000i	− 1.41631i	0.706057	−	0.708155i	$-0.250472\pi$
$338$	− 16.8564i	− 0.916868i
$339$	7.71281	0.418902
$340$	0	0
$341$	−4.00000	−0.216612
$342$	− 15.2679i	− 0.825596i
$343$	− 39.7128i	− 2.14429i
$344$	6.92820	0.373544
$345$	0	0
$346$	−10.0000	−0.537603
$347$	− 30.9282i	− 1.66031i	−0.557530	−	0.830156i	$-0.688251\pi$
$347$	− 30.9282i	− 1.66031i	0.557530	−	0.830156i	$-0.311749\pi$
$348$	3.60770i	0.193393i
$349$	15.3205	0.820088	0.410044	−	0.912066i	$-0.365513\pi$
$349$	15.3205	0.820088	0.410044	+	0.912066i	$0.365513\pi$
$350$	0	0
$351$	21.8564	1.16661
$352$	− 5.46410i	− 0.291238i
$353$	− 11.8564i	− 0.631053i	−0.948917	−	0.315526i	$-0.897819\pi$
$353$	− 11.8564i	− 0.631053i	0.948917	−	0.315526i	$-0.102181\pi$
$354$	−7.46410	−0.396713
$355$	0	0
$356$	−2.00000	−0.106000
$357$	18.9282i	1.00179i
$358$	0.339746i	0.0179561i
$359$	12.3923	0.654041	0.327020	−	0.945017i	$-0.393955\pi$
$359$	12.3923	0.654041	0.327020	+	0.945017i	$0.393955\pi$
$360$	0	0
$361$	19.3923	1.02065
$362$	5.46410i	0.287187i
$363$	13.8038i	0.724514i
$364$	−25.8564	−1.35524
$365$	0	0
$366$	3.60770	0.188577
$367$	4.33975i	0.226533i	0.993565	+	0.113266i	$0.0361314\pi$
$367$	4.33975i	0.226533i	−0.993565	+	0.113266i	$0.963869\pi$
$368$	− 8.00000i	− 0.417029i
$369$	−4.92820	−0.256552
$370$	0	0
$371$	28.3923	1.47406
$372$	− 0.535898i	− 0.0277850i
$373$	− 10.7846i	− 0.558406i	−0.960232	−	0.279203i	$-0.909930\pi$
$373$	− 10.7846i	− 0.558406i	0.960232	−	0.279203i	$-0.0900702\pi$
$374$	−29.8564	−1.54384
$375$	0	0
$376$	4.73205	0.244037
$377$	26.9282i	1.38687i
$378$	− 18.9282i	− 0.973562i
$379$	−32.3923	−1.66388	−0.831940	−	0.554865i	$-0.812770\pi$
$379$	−32.3923	−1.66388	−0.831940	+	0.554865i	$0.812770\pi$
$380$	0	0
$381$	2.67949	0.137275
$382$	− 8.73205i	− 0.446771i
$383$	− 8.00000i	− 0.408781i	−0.978889	−	0.204390i	$-0.934479\pi$
$383$	− 8.00000i	− 0.408781i	0.978889	−	0.204390i	$-0.0655212\pi$
$384$	0.732051	0.0373573
$385$	0	0
$386$	−15.8564	−0.807070
$387$	17.0718i	0.867808i
$388$	− 2.00000i	− 0.101535i
$389$	11.8564	0.601144	0.300572	−	0.953759i	$-0.402822\pi$
$389$	11.8564	0.601144	0.300572	+	0.953759i	$0.402822\pi$
$390$	0	0
$391$	−43.7128	−2.21065
$392$	15.3923i	0.777429i
$393$	− 13.6077i	− 0.686417i
$394$	−22.7846	−1.14787
$395$	0	0
$396$	13.4641	0.676597
$397$	22.0000i	1.10415i	0.833795	+	0.552074i	$0.186163\pi$
$397$	22.0000i	1.10415i	−0.833795	+	0.552074i	$0.813837\pi$
$398$	12.0526i	0.604140i
$399$	21.4641	1.07455
$400$	0	0
$401$	−32.9282	−1.64436	−0.822178	−	0.569230i	$-0.807241\pi$
$401$	−32.9282	−1.64436	−0.822178	+	0.569230i	$0.807241\pi$
$402$	− 2.67949i	− 0.133641i
$403$	− 4.00000i	− 0.199254i
$404$	9.46410	0.470857
$405$	0	0
$406$	23.3205	1.15738
$407$	5.46410i	0.270845i
$408$	− 4.00000i	− 0.198030i
$409$	−3.07180	−0.151891	−0.0759453	−	0.997112i	$-0.524197\pi$
$409$	−3.07180	−0.151891	−0.0759453	+	0.997112i	$0.524197\pi$
$410$	0	0
$411$	1.46410	0.0722188
$412$	6.53590i	0.322001i
$413$	48.2487i	2.37416i
$414$	19.7128	0.968832
$415$	0	0
$416$	5.46410	0.267900
$417$	− 5.07180i	− 0.248367i
$418$	33.8564i	1.65597i
$419$	−14.2487	−0.696095	−0.348048	−	0.937477i	$-0.613155\pi$
$419$	−14.2487	−0.696095	−0.348048	+	0.937477i	$0.613155\pi$
$420$	0	0
$421$	−0.143594	−0.00699832	−0.00349916	−	0.999994i	$-0.501114\pi$
$421$	−0.143594	−0.00699832	−0.00349916	+	0.999994i	$0.501114\pi$
$422$	− 17.8564i	− 0.869236i
$423$	11.6603i	0.566941i
$424$	−6.00000	−0.291386
$425$	0	0
$426$	−2.14359	−0.103857
$427$	− 23.3205i	− 1.12856i
$428$	3.26795i	0.157962i
$429$	−21.8564	−1.05524
$430$	0	0
$431$	−2.19615	−0.105785	−0.0528925	−	0.998600i	$-0.516844\pi$
$431$	−2.19615	−0.105785	−0.0528925	+	0.998600i	$0.516844\pi$
$432$	4.00000i	0.192450i
$433$	− 34.0000i	− 1.63394i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$	− 34.0000i	− 1.63394i	0.576683	−	0.816968i	$-0.304347\pi$
$434$	−3.46410	−0.166282
$435$	0	0
$436$	2.00000	0.0957826
$437$	49.5692i	2.37122i
$438$	0.679492i	0.0324674i
$439$	−13.5167	−0.645115	−0.322558	−	0.946550i	$-0.604543\pi$
$439$	−13.5167	−0.645115	−0.322558	+	0.946550i	$0.604543\pi$
$440$	0	0
$441$	−37.9282	−1.80610
$442$	− 29.8564i	− 1.42012i
$443$	− 14.8756i	− 0.706763i	−0.935479	−	0.353382i	$-0.885032\pi$
$443$	− 14.8756i	− 0.706763i	0.935479	−	0.353382i	$-0.114968\pi$
$444$	−0.732051	−0.0347416
$445$	0	0
$446$	−16.0526	−0.760111
$447$	− 3.21539i	− 0.152083i
$448$	− 4.73205i	− 0.223568i
$449$	21.7128	1.02469	0.512345	−	0.858779i	$-0.328777\pi$
$449$	21.7128	1.02469	0.512345	+	0.858779i	$0.328777\pi$
$450$	0	0
$451$	10.9282	0.514589
$452$	10.5359i	0.495567i
$453$	− 9.07180i	− 0.426230i
$454$	24.3923	1.14479
$455$	0	0
$456$	−4.53590	−0.212413
$457$	31.8564i	1.49018i	0.666964	+	0.745090i	$0.267593\pi$
$457$	31.8564i	1.49018i	−0.666964	+	0.745090i	$0.732407\pi$
$458$	11.8564i	0.554013i
$459$	21.8564	1.02017
$460$	0	0
$461$	14.7846	0.688588	0.344294	−	0.938862i	$-0.388118\pi$
$461$	14.7846	0.688588	0.344294	+	0.938862i	$0.388118\pi$
$462$	18.9282i	0.880620i
$463$	18.9282i	0.879668i	0.898079	+	0.439834i	$0.144963\pi$
$463$	18.9282i	0.879668i	−0.898079	+	0.439834i	$0.855037\pi$
$464$	−4.92820	−0.228786
$465$	0	0
$466$	−28.9282	−1.34007
$467$	25.1769i	1.16505i	0.812813	+	0.582524i	$0.197935\pi$
$467$	25.1769i	1.16505i	−0.812813	+	0.582524i	$0.802065\pi$
$468$	13.4641i	0.622378i
$469$	−17.3205	−0.799787
$470$	0	0
$471$	2.24871	0.103615
$472$	− 10.1962i	− 0.469316i
$473$	− 37.8564i	− 1.74064i
$474$	6.39230	0.293608
$475$	0	0
$476$	−25.8564	−1.18513
$477$	− 14.7846i	− 0.676941i
$478$	20.7321i	0.948262i
$479$	−4.05256	−0.185166	−0.0925831	−	0.995705i	$-0.529512\pi$
$479$	−4.05256	−0.185166	−0.0925831	+	0.995705i	$0.529512\pi$
$480$	0	0
$481$	−5.46410	−0.249142
$482$	4.92820i	0.224474i
$483$	27.7128i	1.26098i
$484$	−18.8564	−0.857109
$485$	0	0
$486$	−15.2679	−0.692568
$487$	− 4.39230i	− 0.199034i	−0.995036	−	0.0995172i	$-0.968270\pi$
$487$	− 4.39230i	− 0.199034i	0.995036	−	0.0995172i	$-0.0317298\pi$
$488$	4.92820i	0.223089i
$489$	8.28719	0.374760
$490$	0	0
$491$	−14.9282	−0.673700	−0.336850	−	0.941558i	$-0.609362\pi$
$491$	−14.9282	−0.673700	−0.336850	+	0.941558i	$0.609362\pi$
$492$	1.46410i	0.0660068i
$493$	26.9282i	1.21279i
$494$	−33.8564	−1.52327
$495$	0	0
$496$	0.732051	0.0328701
$497$	13.8564i	0.621545i
$498$	6.39230i	0.286446i
$499$	−9.41154	−0.421319	−0.210659	−	0.977560i	$-0.567561\pi$
$499$	−9.41154	−0.421319	−0.210659	+	0.977560i	$0.567561\pi$
$500$	0	0
$501$	−1.07180	−0.0478843
$502$	19.2679i	0.859971i
$503$	− 18.9282i	− 0.843967i	−0.906604	−	0.421983i	$-0.861334\pi$
$503$	− 18.9282i	− 0.843967i	0.906604	−	0.421983i	$-0.138666\pi$
$504$	11.6603	0.519389
$505$	0	0
$506$	−43.7128	−1.94327
$507$	− 12.3397i	− 0.548027i
$508$	3.66025i	0.162398i
$509$	2.00000	0.0886484	0.0443242	−	0.999017i	$-0.485887\pi$
$509$	2.00000	0.0886484	0.0443242	+	0.999017i	$0.485887\pi$
$510$	0	0
$511$	4.39230	0.194304
$512$	1.00000i	0.0441942i
$513$	− 24.7846i	− 1.09427i
$514$	−18.5359	−0.817583
$515$	0	0
$516$	5.07180	0.223273
$517$	− 25.8564i	− 1.13716i
$518$	4.73205i	0.207914i
$519$	−7.32051	−0.321335
$520$	0	0
$521$	26.5359	1.16256	0.581279	−	0.813704i	$-0.302552\pi$
$521$	26.5359	1.16256	0.581279	+	0.813704i	$0.302552\pi$
$522$	− 12.1436i	− 0.531511i
$523$	36.7846i	1.60848i	0.594306	+	0.804239i	$0.297427\pi$
$523$	36.7846i	1.60848i	−0.594306	+	0.804239i	$0.702573\pi$
$524$	18.5885	0.812041
$525$	0	0
$526$	8.05256	0.351108
$527$	− 4.00000i	− 0.174243i
$528$	− 4.00000i	− 0.174078i
$529$	−41.0000	−1.78261
$530$	0	0
$531$	25.1244	1.09030
$532$	29.3205i	1.27121i
$533$	10.9282i	0.473353i
$534$	−1.46410	−0.0633579
$535$	0	0
$536$	3.66025	0.158099
$537$	0.248711i	0.0107327i
$538$	− 20.3923i	− 0.879175i
$539$	84.1051	3.62266
$540$	0	0
$541$	−30.0000	−1.28980	−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000	−1.28980	−0.644900	+	0.764267i	$0.723101\pi$
$542$	− 24.7846i	− 1.06459i
$543$	4.00000i	0.171656i
$544$	5.46410	0.234271
$545$	0	0
$546$	−18.9282	−0.810052
$547$	4.00000i	0.171028i	0.996337	+	0.0855138i	$0.0272532\pi$
$547$	4.00000i	0.171028i	−0.996337	+	0.0855138i	$0.972747\pi$
$548$	2.00000i	0.0854358i
$549$	−12.1436	−0.518276
$550$	0	0
$551$	30.5359	1.30087
$552$	− 5.85641i	− 0.249265i
$553$	− 41.3205i	− 1.75713i
$554$	22.2487	0.945257
$555$	0	0
$556$	6.92820	0.293821
$557$	− 44.1051i	− 1.86879i	−0.356234	−	0.934397i	$-0.615939\pi$
$557$	− 44.1051i	− 1.86879i	0.356234	−	0.934397i	$-0.384061\pi$
$558$	1.80385i	0.0763630i
$559$	37.8564	1.60116
$560$	0	0
$561$	−21.8564	−0.922778
$562$	− 8.92820i	− 0.376614i
$563$	30.9282i	1.30347i	0.758447	+	0.651734i	$0.225958\pi$
$563$	30.9282i	1.30347i	−0.758447	+	0.651734i	$0.774042\pi$
$564$	3.46410	0.145865
$565$	0	0
$566$	−16.3923	−0.689020
$567$	21.1244i	0.887140i
$568$	− 2.92820i	− 0.122865i
$569$	22.0000	0.922288	0.461144	−	0.887325i	$-0.347439\pi$
$569$	22.0000	0.922288	0.461144	+	0.887325i	$0.347439\pi$
$570$	0	0
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	− 29.8564i	− 1.24836i
$573$	− 6.39230i	− 0.267042i
$574$	9.46410	0.395024
$575$	0	0
$576$	−2.46410	−0.102671
$577$	24.3923i	1.01546i	0.861515	+	0.507732i	$0.169516\pi$
$577$	24.3923i	1.01546i	−0.861515	+	0.507732i	$0.830484\pi$
$578$	− 12.8564i	− 0.534756i
$579$	−11.6077	−0.482399
$580$	0	0
$581$	41.3205	1.71426
$582$	− 1.46410i	− 0.0606890i
$583$	32.7846i	1.35780i
$584$	−0.928203	−0.0384093
$585$	0	0
$586$	−6.00000	−0.247858
$587$	− 44.7846i	− 1.84846i	−0.381838	−	0.924229i	$-0.624709\pi$
$587$	− 44.7846i	− 1.84846i	0.381838	−	0.924229i	$-0.375291\pi$
$588$	11.2679i	0.464682i
$589$	−4.53590	−0.186898
$590$	0	0
$591$	−16.6795	−0.686103
$592$	− 1.00000i	− 0.0410997i
$593$	− 34.7846i	− 1.42843i	−0.699925	−	0.714216i	$-0.746783\pi$
$593$	− 34.7846i	− 1.42843i	0.699925	−	0.714216i	$-0.253217\pi$
$594$	21.8564	0.896779
$595$	0	0
$596$	4.39230	0.179916
$597$	8.82309i	0.361105i
$598$	− 43.7128i	− 1.78755i
$599$	−9.46410	−0.386693	−0.193346	−	0.981131i	$-0.561934\pi$
$599$	−9.46410	−0.386693	−0.193346	+	0.981131i	$0.561934\pi$
$600$	0	0
$601$	27.6077	1.12614	0.563071	−	0.826409i	$-0.309620\pi$
$601$	27.6077	1.12614	0.563071	+	0.826409i	$0.309620\pi$
$602$	− 32.7846i	− 1.33620i
$603$	9.01924i	0.367292i
$604$	12.3923	0.504236
$605$	0	0
$606$	6.92820	0.281439
$607$	− 0.784610i	− 0.0318463i	−0.999873	−	0.0159232i	$-0.994931\pi$
$607$	− 0.784610i	− 0.0318463i	0.999873	−	0.0159232i	$-0.00506871\pi$
$608$	− 6.19615i	− 0.251287i
$609$	17.0718	0.691784
$610$	0	0
$611$	25.8564	1.04604
$612$	13.4641i	0.544254i
$613$	16.9282i	0.683724i	0.939750	+	0.341862i	$0.111057\pi$
$613$	16.9282i	0.683724i	−0.939750	+	0.341862i	$0.888943\pi$
$614$	18.5885	0.750169
$615$	0	0
$616$	−25.8564	−1.04178
$617$	0.928203i	0.0373681i	0.999825	+	0.0186840i	$0.00594766\pi$
$617$	0.928203i	0.0373681i	−0.999825	+	0.0186840i	$0.994052\pi$
$618$	4.78461i	0.192465i
$619$	17.8564	0.717710	0.358855	−	0.933393i	$-0.383167\pi$
$619$	17.8564	0.717710	0.358855	+	0.933393i	$0.383167\pi$
$620$	0	0
$621$	32.0000	1.28412
$622$	2.87564i	0.115303i
$623$	9.46410i	0.379171i
$624$	4.00000	0.160128
$625$	0	0
$626$	23.8564	0.953494
$627$	24.7846i	0.989802i
$628$	3.07180i	0.122578i
$629$	−5.46410	−0.217868
$630$	0	0
$631$	30.9808	1.23332	0.616662	−	0.787228i	$-0.288484\pi$
$631$	30.9808	1.23332	0.616662	+	0.787228i	$0.288484\pi$
$632$	8.73205i	0.347342i
$633$	− 13.0718i	− 0.519557i
$634$	−4.14359	−0.164563
$635$	0	0
$636$	−4.39230	−0.174166
$637$	84.1051i	3.33237i
$638$	26.9282i	1.06610i
$639$	7.21539	0.285436
$640$	0	0
$641$	−6.53590	−0.258152	−0.129076	−	0.991635i	$-0.541201\pi$
$641$	−6.53590	−0.258152	−0.129076	+	0.991635i	$0.541201\pi$
$642$	2.39230i	0.0944167i
$643$	34.5359i	1.36196i	0.732301	+	0.680981i	$0.238447\pi$
$643$	34.5359i	1.36196i	−0.732301	+	0.680981i	$0.761553\pi$
$644$	−37.8564	−1.49175
$645$	0	0
$646$	−33.8564	−1.33206
$647$	35.7128i	1.40402i	0.712169	+	0.702008i	$0.247713\pi$
$647$	35.7128i	1.40402i	−0.712169	+	0.702008i	$0.752287\pi$
$648$	− 4.46410i	− 0.175366i
$649$	−55.7128	−2.18692
$650$	0	0
$651$	−2.53590	−0.0993897
$652$	11.3205i	0.443345i
$653$	− 18.0000i	− 0.704394i	−0.935926	−	0.352197i	$-0.885435\pi$
$653$	− 18.0000i	− 0.704394i	0.935926	−	0.352197i	$-0.114565\pi$
$654$	1.46410	0.0572509
$655$	0	0
$656$	−2.00000	−0.0780869
$657$	− 2.28719i	− 0.0892317i
$658$	− 22.3923i	− 0.872943i
$659$	6.92820	0.269884	0.134942	−	0.990853i	$-0.456915\pi$
$659$	6.92820	0.269884	0.134942	+	0.990853i	$0.456915\pi$
$660$	0	0
$661$	−31.0718	−1.20855	−0.604276	−	0.796775i	$-0.706538\pi$
$661$	−31.0718	−1.20855	−0.604276	+	0.796775i	$0.706538\pi$
$662$	− 33.1244i	− 1.28741i
$663$	− 21.8564i	− 0.848832i
$664$	−8.73205	−0.338869
$665$	0	0
$666$	2.46410	0.0954820
$667$	39.4256i	1.52657i
$668$	− 1.46410i	− 0.0566478i
$669$	−11.7513	−0.454331
$670$	0	0
$671$	26.9282	1.03955
$672$	− 3.46410i	− 0.133631i
$673$	− 32.9282i	− 1.26929i	−0.772804	−	0.634644i	$-0.781147\pi$
$673$	− 32.9282i	− 1.26929i	0.772804	−	0.634644i	$-0.218853\pi$
$674$	26.0000	1.00148
$675$	0	0
$676$	16.8564	0.648323
$677$	4.14359i	0.159251i	0.996825	+	0.0796256i	$0.0253725\pi$
$677$	4.14359i	0.159251i	−0.996825	+	0.0796256i	$0.974628\pi$
$678$	7.71281i	0.296209i
$679$	−9.46410	−0.363199
$680$	0	0
$681$	17.8564	0.684259
$682$	− 4.00000i	− 0.153168i
$683$	− 4.78461i	− 0.183078i	−0.995801	−	0.0915390i	$-0.970821\pi$
$683$	− 4.78461i	− 0.183078i	0.995801	−	0.0915390i	$-0.0291786\pi$
$684$	15.2679	0.583785
$685$	0	0
$686$	39.7128	1.51624
$687$	8.67949i	0.331143i
$688$	6.92820i	0.264135i
$689$	−32.7846	−1.24899
$690$	0	0
$691$	−0.392305	−0.0149240	−0.00746199	−	0.999972i	$-0.502375\pi$
$691$	−0.392305	−0.0149240	−0.00746199	+	0.999972i	$0.502375\pi$
$692$	− 10.0000i	− 0.380143i
$693$	− 63.7128i	− 2.42025i
$694$	30.9282	1.17402
$695$	0	0
$696$	−3.60770	−0.136749
$697$	10.9282i	0.413935i
$698$	15.3205i	0.579890i
$699$	−21.1769	−0.800984
$700$	0	0
$701$	−11.8564	−0.447810	−0.223905	−	0.974611i	$-0.571881\pi$
$701$	−11.8564	−0.447810	−0.223905	+	0.974611i	$0.571881\pi$
$702$	21.8564i	0.824917i
$703$	6.19615i	0.233692i
$704$	5.46410	0.205936
$705$	0	0
$706$	11.8564	0.446222
$707$	− 44.7846i	− 1.68430i
$708$	− 7.46410i	− 0.280518i
$709$	−43.8564	−1.64706	−0.823531	−	0.567271i	$-0.807999\pi$
$709$	−43.8564	−1.64706	−0.823531	+	0.567271i	$0.807999\pi$
$710$	0	0
$711$	−21.5167	−0.806938
$712$	− 2.00000i	− 0.0749532i
$713$	− 5.85641i	− 0.219324i
$714$	−18.9282	−0.708370
$715$	0	0
$716$	−0.339746	−0.0126969
$717$	15.1769i	0.566792i
$718$	12.3923i	0.462477i
$719$	12.3923	0.462155	0.231077	−	0.972935i	$-0.425775\pi$
$719$	12.3923	0.462155	0.231077	+	0.972935i	$0.425775\pi$
$720$	0	0
$721$	30.9282	1.15183
$722$	19.3923i	0.721707i
$723$	3.60770i	0.134172i
$724$	−5.46410	−0.203072
$725$	0	0
$726$	−13.8038	−0.512309
$727$	− 8.78461i	− 0.325803i	−0.986642	−	0.162902i	$-0.947915\pi$
$727$	− 8.78461i	− 0.325803i	0.986642	−	0.162902i	$-0.0520853\pi$
$728$	− 25.8564i	− 0.958302i
$729$	2.21539	0.0820515
$730$	0	0
$731$	37.8564	1.40017
$732$	3.60770i	0.133344i
$733$	27.8564i	1.02890i	0.857520	+	0.514450i	$0.172004\pi$
$733$	27.8564i	1.02890i	−0.857520	+	0.514450i	$0.827996\pi$
$734$	−4.33975	−0.160183
$735$	0	0
$736$	8.00000	0.294884
$737$	− 20.0000i	− 0.736709i
$738$	− 4.92820i	− 0.181410i
$739$	−6.92820	−0.254858	−0.127429	−	0.991848i	$-0.540673\pi$
$739$	−6.92820	−0.254858	−0.127429	+	0.991848i	$0.540673\pi$
$740$	0	0
$741$	−24.7846	−0.910485
$742$	28.3923i	1.04231i
$743$	17.1244i	0.628232i	0.949385	+	0.314116i	$0.101708\pi$
$743$	17.1244i	0.628232i	−0.949385	+	0.314116i	$0.898292\pi$
$744$	0.535898	0.0196470
$745$	0	0
$746$	10.7846	0.394853
$747$	− 21.5167i	− 0.787253i
$748$	− 29.8564i	− 1.09166i
$749$	15.4641	0.565046
$750$	0	0
$751$	−20.3923	−0.744126	−0.372063	−	0.928208i	$-0.621349\pi$
$751$	−20.3923	−0.744126	−0.372063	+	0.928208i	$0.621349\pi$
$752$	4.73205i	0.172560i
$753$	14.1051i	0.514019i
$754$	−26.9282	−0.980667
$755$	0	0
$756$	18.9282	0.688412
$757$	− 1.71281i	− 0.0622532i	−0.999515	−	0.0311266i	$-0.990090\pi$
$757$	− 1.71281i	− 0.0622532i	0.999515	−	0.0311266i	$-0.00990951\pi$
$758$	− 32.3923i	− 1.17654i
$759$	−32.0000	−1.16153
$760$	0	0
$761$	10.0000	0.362500	0.181250	−	0.983437i	$-0.441986\pi$
$761$	10.0000	0.362500	0.181250	+	0.983437i	$0.441986\pi$
$762$	2.67949i	0.0970678i
$763$	− 9.46410i	− 0.342623i
$764$	8.73205	0.315915
$765$	0	0
$766$	8.00000	0.289052
$767$	− 55.7128i	− 2.01167i
$768$	0.732051i	0.0264156i
$769$	−7.07180	−0.255016	−0.127508	−	0.991838i	$-0.540698\pi$
$769$	−7.07180	−0.255016	−0.127508	+	0.991838i	$0.540698\pi$
$770$	0	0
$771$	−13.5692	−0.488683
$772$	− 15.8564i	− 0.570685i
$773$	2.78461i	0.100155i	0.998745	+	0.0500777i	$0.0159469\pi$
$773$	2.78461i	0.100155i	−0.998745	+	0.0500777i	$0.984053\pi$
$774$	−17.0718	−0.613633
$775$	0	0
$776$	2.00000	0.0717958
$777$	3.46410i	0.124274i
$778$	11.8564i	0.425073i
$779$	12.3923	0.444000
$780$	0	0
$781$	−16.0000	−0.572525
$782$	− 43.7128i	− 1.56317i
$783$	− 19.7128i	− 0.704478i
$784$	−15.3923	−0.549725
$785$	0	0
$786$	13.6077	0.485370
$787$	− 22.1962i	− 0.791207i	−0.918421	−	0.395604i	$-0.870535\pi$
$787$	− 22.1962i	− 0.791207i	0.918421	−	0.395604i	$-0.129465\pi$
$788$	− 22.7846i	− 0.811668i
$789$	5.89488	0.209863
$790$	0	0
$791$	49.8564	1.77269
$792$	13.4641i	0.478426i
$793$	26.9282i	0.956249i
$794$	−22.0000	−0.780751
$795$	0	0
$796$	−12.0526	−0.427192
$797$	− 10.5359i	− 0.373201i	−0.982436	−	0.186600i	$-0.940253\pi$
$797$	− 10.5359i	− 0.373201i	0.982436	−	0.186600i	$-0.0597469\pi$
$798$	21.4641i	0.759821i
$799$	25.8564	0.914734
$800$	0	0
$801$	4.92820	0.174129
$802$	− 32.9282i	− 1.16274i
$803$	5.07180i	0.178980i
$804$	2.67949	0.0944984
$805$	0	0
$806$	4.00000	0.140894
$807$	− 14.9282i	− 0.525498i
$808$	9.46410i	0.332946i
$809$	−43.5692	−1.53181	−0.765906	−	0.642952i	$-0.777709\pi$
$809$	−43.5692	−1.53181	−0.765906	+	0.642952i	$0.777709\pi$
$810$	0	0
$811$	−41.8564	−1.46978	−0.734889	−	0.678188i	$-0.762766\pi$
$811$	−41.8564	−1.46978	−0.734889	+	0.678188i	$0.762766\pi$
$812$	23.3205i	0.818389i
$813$	− 18.1436i	− 0.636324i
$814$	−5.46410	−0.191517
$815$	0	0
$816$	4.00000	0.140028
$817$	− 42.9282i	− 1.50187i
$818$	− 3.07180i	− 0.107403i
$819$	63.7128	2.22631
$820$	0	0
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	1.46410i	0.0510664i
$823$	48.4449i	1.68868i	0.535806	+	0.844341i	$0.320008\pi$
$823$	48.4449i	1.68868i	−0.535806	+	0.844341i	$0.679992\pi$
$824$	−6.53590	−0.227689
$825$	0	0
$826$	−48.2487	−1.67879
$827$	16.3923i	0.570016i	0.958525	+	0.285008i	$0.0919963\pi$
$827$	16.3923i	0.570016i	−0.958525	+	0.285008i	$0.908004\pi$
$828$	19.7128i	0.685068i
$829$	51.5692	1.79107	0.895537	−	0.444988i	$-0.146792\pi$
$829$	51.5692	1.79107	0.895537	+	0.444988i	$0.146792\pi$
$830$	0	0
$831$	16.2872	0.564996
$832$	5.46410i	0.189434i
$833$	84.1051i	2.91407i
$834$	5.07180	0.175622
$835$	0	0
$836$	−33.8564	−1.17095
$837$	2.92820i	0.101214i
$838$	− 14.2487i	− 0.492214i
$839$	8.78461	0.303278	0.151639	−	0.988436i	$-0.451545\pi$
$839$	8.78461	0.303278	0.151639	+	0.988436i	$0.451545\pi$
$840$	0	0
$841$	−4.71281	−0.162511
$842$	− 0.143594i	− 0.00494856i
$843$	− 6.53590i	− 0.225108i
$844$	17.8564	0.614643
$845$	0	0
$846$	−11.6603	−0.400888
$847$	89.2295i	3.06596i
$848$	− 6.00000i	− 0.206041i
$849$	−12.0000	−0.411839
$850$	0	0
$851$	−8.00000	−0.274236
$852$	− 2.14359i	− 0.0734383i
$853$	− 30.0000i	− 1.02718i	−0.858036	−	0.513590i	$-0.828315\pi$
$853$	− 30.0000i	− 1.02718i	0.858036	−	0.513590i	$-0.171685\pi$
$854$	23.3205	0.798011
$855$	0	0
$856$	−3.26795	−0.111696
$857$	31.8564i	1.08819i	0.839022	+	0.544097i	$0.183128\pi$
$857$	31.8564i	1.08819i	−0.839022	+	0.544097i	$0.816872\pi$
$858$	− 21.8564i	− 0.746165i
$859$	−44.4449	−1.51644	−0.758220	−	0.651999i	$-0.773931\pi$
$859$	−44.4449	−1.51644	−0.758220	+	0.651999i	$0.773931\pi$
$860$	0	0
$861$	6.92820	0.236113
$862$	− 2.19615i	− 0.0748012i
$863$	− 20.4449i	− 0.695951i	−0.937504	−	0.347976i	$-0.886869\pi$
$863$	− 20.4449i	− 0.695951i	0.937504	−	0.347976i	$-0.113131\pi$
$864$	−4.00000	−0.136083
$865$	0	0
$866$	34.0000	1.15537
$867$	− 9.41154i	− 0.319633i
$868$	− 3.46410i	− 0.117579i
$869$	47.7128	1.61855
$870$	0	0
$871$	20.0000	0.677674
$872$	2.00000i	0.0677285i
$873$	4.92820i	0.166794i
$874$	−49.5692	−1.67670
$875$	0	0
$876$	−0.679492	−0.0229579
$877$	9.21539i	0.311182i	0.987822	+	0.155591i	$0.0497281\pi$
$877$	9.21539i	0.311182i	−0.987822	+	0.155591i	$0.950272\pi$
$878$	− 13.5167i	− 0.456165i
$879$	−4.39230	−0.148149
$880$	0	0
$881$	12.6795	0.427183	0.213591	−	0.976923i	$-0.431484\pi$
$881$	12.6795	0.427183	0.213591	+	0.976923i	$0.431484\pi$
$882$	− 37.9282i	− 1.27711i
$883$	14.2487i	0.479507i	0.970834	+	0.239754i	$0.0770667\pi$
$883$	14.2487i	0.479507i	−0.970834	+	0.239754i	$0.922933\pi$
$884$	29.8564	1.00418
$885$	0	0
$886$	14.8756	0.499757
$887$	− 9.80385i	− 0.329181i	−0.986362	−	0.164590i	$-0.947370\pi$
$887$	− 9.80385i	− 0.329181i	0.986362	−	0.164590i	$-0.0526303\pi$
$888$	− 0.732051i	− 0.0245660i
$889$	17.3205	0.580911
$890$	0	0
$891$	−24.3923	−0.817173
$892$	− 16.0526i	− 0.537479i
$893$	− 29.3205i	− 0.981173i
$894$	3.21539	0.107539
$895$	0	0
$896$	4.73205	0.158087
$897$	− 32.0000i	− 1.06845i
$898$	21.7128i	0.724566i
$899$	−3.60770	−0.120323
$900$	0	0
$901$	−32.7846	−1.09221
$902$	10.9282i	0.363869i
$903$	− 24.0000i	− 0.798670i
$904$	−10.5359	−0.350419
$905$	0	0
$906$	9.07180	0.301390
$907$	− 54.2487i	− 1.80130i	−0.434546	−	0.900649i	$-0.643091\pi$
$907$	− 54.2487i	− 1.80130i	0.434546	−	0.900649i	$-0.356909\pi$
$908$	24.3923i	0.809487i
$909$	−23.3205	−0.773492
$910$	0	0
$911$	37.9090	1.25598	0.627990	−	0.778221i	$-0.283878\pi$
$911$	37.9090	1.25598	0.627990	+	0.778221i	$0.283878\pi$
$912$	− 4.53590i	− 0.150199i
$913$	47.7128i	1.57906i
$914$	−31.8564	−1.05372
$915$	0	0
$916$	−11.8564	−0.391747
$917$	− 87.9615i	− 2.90475i
$918$	21.8564i	0.721369i
$919$	16.7321	0.551939	0.275970	−	0.961166i	$-0.411001\pi$
$919$	16.7321	0.551939	0.275970	+	0.961166i	$0.411001\pi$
$920$	0	0
$921$	13.6077	0.448389
$922$	14.7846i	0.486905i
$923$	− 16.0000i	− 0.526646i
$924$	−18.9282	−0.622692
$925$	0	0
$926$	−18.9282	−0.622019
$927$	− 16.1051i	− 0.528961i
$928$	− 4.92820i	− 0.161776i
$929$	−11.8564	−0.388996	−0.194498	−	0.980903i	$-0.562308\pi$
$929$	−11.8564	−0.388996	−0.194498	+	0.980903i	$0.562308\pi$
$930$	0	0
$931$	95.3731	3.12573
$932$	− 28.9282i	− 0.947575i
$933$	2.10512i	0.0689185i
$934$	−25.1769	−0.823814
$935$	0	0
$936$	−13.4641	−0.440088
$937$	23.8564i	0.779355i	0.920951	+	0.389677i	$0.127413\pi$
$937$	23.8564i	0.779355i	−0.920951	+	0.389677i	$0.872587\pi$
$938$	− 17.3205i	− 0.565535i
$939$	17.4641	0.569919
$940$	0	0
$941$	7.60770	0.248004	0.124002	−	0.992282i	$-0.460427\pi$
$941$	7.60770	0.248004	0.124002	+	0.992282i	$0.460427\pi$
$942$	2.24871i	0.0732670i
$943$	16.0000i	0.521032i
$944$	10.1962	0.331856
$945$	0	0
$946$	37.8564	1.23082
$947$	− 17.1769i	− 0.558175i	−0.960266	−	0.279087i	$-0.909968\pi$
$947$	− 17.1769i	− 0.558175i	0.960266	−	0.279087i	$-0.0900319\pi$
$948$	6.39230i	0.207612i
$949$	−5.07180	−0.164637
$950$	0	0
$951$	−3.03332	−0.0983622
$952$	− 25.8564i	− 0.838011i
$953$	15.8564i	0.513639i	0.966459	+	0.256820i	$0.0826747\pi$
$953$	15.8564i	0.513639i	−0.966459	+	0.256820i	$0.917325\pi$
$954$	14.7846	0.478669
$955$	0	0
$956$	−20.7321	−0.670522
$957$	19.7128i	0.637225i
$958$	− 4.05256i	− 0.130932i
$959$	9.46410	0.305612
$960$	0	0
$961$	−30.4641	−0.982713
$962$	− 5.46410i	− 0.176170i
$963$	− 8.05256i	− 0.259490i
$964$	−4.92820	−0.158727
$965$	0	0
$966$	−27.7128	−0.891645
$967$	44.3923i	1.42756i	0.700370	+	0.713780i	$0.253018\pi$
$967$	44.3923i	1.42756i	−0.700370	+	0.713780i	$0.746982\pi$
$968$	− 18.8564i	− 0.606068i
$969$	−24.7846	−0.796196
$970$	0	0
$971$	1.07180	0.0343956	0.0171978	−	0.999852i	$-0.494526\pi$
$971$	1.07180	0.0343956	0.0171978	+	0.999852i	$0.494526\pi$
$972$	− 15.2679i	− 0.489720i
$973$	− 32.7846i	− 1.05103i
$974$	4.39230	0.140739
$975$	0	0
$976$	−4.92820	−0.157748
$977$	34.0000i	1.08776i	0.839164	+	0.543878i	$0.183045\pi$
$977$	34.0000i	1.08776i	−0.839164	+	0.543878i	$0.816955\pi$
$978$	8.28719i	0.264995i
$979$	−10.9282	−0.349267
$980$	0	0
$981$	−4.92820	−0.157345
$982$	− 14.9282i	− 0.476378i
$983$	20.4449i	0.652090i	0.945354	+	0.326045i	$0.105716\pi$
$983$	20.4449i	0.652090i	−0.945354	+	0.326045i	$0.894284\pi$
$984$	−1.46410	−0.0466739
$985$	0	0
$986$	−26.9282	−0.857569
$987$	− 16.3923i	− 0.521773i
$988$	− 33.8564i	− 1.07712i
$989$	55.4256	1.76243
$990$	0	0
$991$	44.0526	1.39938	0.699688	−	0.714449i	$-0.253322\pi$
$991$	44.0526	1.39938	0.699688	+	0.714449i	$0.253322\pi$
$992$	0.732051i	0.0232426i
$993$	− 24.2487i	− 0.769510i
$994$	−13.8564	−0.439499
$995$	0	0
$996$	−6.39230	−0.202548
$997$	31.8564i	1.00890i	0.863440	+	0.504451i	$0.168305\pi$
$997$	31.8564i	1.00890i	−0.863440	+	0.504451i	$0.831695\pi$
$998$	− 9.41154i	− 0.297917i
$999$	4.00000	0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.b.l.149.4		4
5.2	odd	4		370.2.a.e.1.2	✓	2
5.3	odd	4		1850.2.a.x.1.1		2
5.4	even	2	inner	1850.2.b.l.149.1		4
15.2	even	4		3330.2.a.bd.1.1		2
20.7	even	4		2960.2.a.q.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.a.e.1.2	✓	2	5.2	odd	4
1850.2.a.x.1.1		2	5.3	odd	4
1850.2.b.l.149.1		4	5.4	even	2	inner
1850.2.b.l.149.4		4	1.1	even	1	trivial
2960.2.a.q.1.1		2	20.7	even	4
3330.2.a.bd.1.1		2	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +0.732051i q^{3} -1.00000 q^{4} -0.732051 q^{6} +4.73205i q^{7} -1.00000i q^{8} +2.46410 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +0.732051i q^{3} -1.00000 q^{4} -0.732051 q^{6} +4.73205i q^{7} -1.00000i q^{8} +2.46410 q^{9} -5.46410 q^{11} -0.732051i q^{12} -5.46410i q^{13} -4.73205 q^{14} +1.00000 q^{16} -5.46410i q^{17} +2.46410i q^{18} -6.19615 q^{19} -3.46410 q^{21} -5.46410i q^{22} -8.00000i q^{23} +0.732051 q^{24} +5.46410 q^{26} +4.00000i q^{27} -4.73205i q^{28} -4.92820 q^{29} +0.732051 q^{31} +1.00000i q^{32} -4.00000i q^{33} +5.46410 q^{34} -2.46410 q^{36} -1.00000i q^{37} -6.19615i q^{38} +4.00000 q^{39} -2.00000 q^{41} -3.46410i q^{42} +6.92820i q^{43} +5.46410 q^{44} +8.00000 q^{46} +4.73205i q^{47} +0.732051i q^{48} -15.3923 q^{49} +4.00000 q^{51} +5.46410i q^{52} -6.00000i q^{53} -4.00000 q^{54} +4.73205 q^{56} -4.53590i q^{57} -4.92820i q^{58} +10.1962 q^{59} -4.92820 q^{61} +0.732051i q^{62} +11.6603i q^{63} -1.00000 q^{64} +4.00000 q^{66} +3.66025i q^{67} +5.46410i q^{68} +5.85641 q^{69} +2.92820 q^{71} -2.46410i q^{72} -0.928203i q^{73} +1.00000 q^{74} +6.19615 q^{76} -25.8564i q^{77} +4.00000i q^{78} -8.73205 q^{79} +4.46410 q^{81} -2.00000i q^{82} -8.73205i q^{83} +3.46410 q^{84} -6.92820 q^{86} -3.60770i q^{87} +5.46410i q^{88} +2.00000 q^{89} +25.8564 q^{91} +8.00000i q^{92} +0.535898i q^{93} -4.73205 q^{94} -0.732051 q^{96} +2.00000i q^{97} -15.3923i q^{98} -13.4641 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} - 8 q^{11} - 12 q^{14} + 4 q^{16} - 4 q^{19} - 4 q^{24} + 8 q^{26} + 8 q^{29} - 4 q^{31} + 8 q^{34} + 4 q^{36} + 16 q^{39} - 8 q^{41} + 8 q^{44} + 32 q^{46} - 20 q^{49} + 16 q^{51} - 16 q^{54} + 12 q^{56} + 20 q^{59} + 8 q^{61} - 4 q^{64} + 16 q^{66} - 32 q^{69} - 16 q^{71} + 4 q^{74} + 4 q^{76} - 28 q^{79} + 4 q^{81} + 8 q^{89} + 48 q^{91} - 12 q^{94} + 4 q^{96} - 40 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 - 8 * q^11 - 12 * q^14 + 4 * q^16 - 4 * q^19 - 4 * q^24 + 8 * q^26 + 8 * q^29 - 4 * q^31 + 8 * q^34 + 4 * q^36 + 16 * q^39 - 8 * q^41 + 8 * q^44 + 32 * q^46 - 20 * q^49 + 16 * q^51 - 16 * q^54 + 12 * q^56 + 20 * q^59 + 8 * q^61 - 4 * q^64 + 16 * q^66 - 32 * q^69 - 16 * q^71 + 4 * q^74 + 4 * q^76 - 28 * q^79 + 4 * q^81 + 8 * q^89 + 48 * q^91 - 12 * q^94 + 4 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more